Problem: Sam used $6$ loaves of elf bread on an $8$ day hiking trip. He wants to know how many loaves of elf bread $(b)$ he should pack for a $12$ day hiking trip if he eats the same amount of bread each day. How many loaves of elf bread should Sam pack for a $12$ day trip?
Answer: We're dealing with a proportional relationship, so each ratio of loaves to days must be equivalent. Here's one way to write the proportion: $\dfrac{b\text{ loaves}}{12\text{ days}} = \dfrac{6\text{ loaves}}{8\text{ days}}$ Now, solve the proportion for $b$ : $\begin{aligned} \dfrac{b}{12} &= \dfrac{6}{8} \\\\ \dfrac{b}{12} &= \dfrac{3}{4} \\\\ b &= \dfrac{3}{4} \cdot 12 \\\\ b &= \dfrac{3\cdot 12}{4} \\\\ b &= \dfrac{3\cdot \stackrel{3}{\cancel{12}} }{\underset{1}{\cancel4}} \\\\ b &= \dfrac{3 \cdot 3}{1} \\\\ b &= \dfrac{9}{1} \\\\ b &= 9 \end{aligned}$ Sam should pack $9$ loaves of elf bread for a $12$ day trip.